We review the present situation in top quark physics, in these early days
of Run II of the LHC. We take mostly a Standard Model
perspective, showing recent results, and review the
key concepts and results of the associated theoretical predictions.
The issues we discuss are the top quark mass,
top quark pair and single top production, production in
association with other particles, charge asymmetry and top quark decay.

1 Introduction

Ever since its discovery[1, 2]
in 1995 by the CDF and D0 experiments at the Tevatron, the top
quark has been in or near the center of attention in high-energy phyiscs. Its
remarkably large mass, still the largest of any known elementary particle,
implies that it couples strongly to the agents of electroweak symmetry breaking,
making it both an object of interest itself, and a tool to investigate that
mechanism in detail.

The history of heavy flavours anyway is such
each of them has taught us much about Nature. From the charm quark we learned
that the Standard Model is consistent, through the GIM [3]
mechanism. Moreover, its discovery cemented the belief in QCD as the
quantum theory of the strong interactions. From the bottom quark we
learned that a complete third family was there to find, in turn
allowing for weak CP violation [4]
to be part of the Standard Model. However,
although already discovered 20 years ago, the top quark has not yet taught
us fundamentally new insights. The top may well do this
in the coming decade after all, a belief that rests on top’s attributes.

The top quark couples to other particles
through various (chiral, vector, scalar) structures according to the Standard
Model Lagrangian. In our search for physics beyond the Standard Model,
all of these bear scrutiny for deviations, and there is therefore
much to test. Such precise scrutiny is feasible because the large top mass
implies that hadronization effects do not occur and spin information is preserved.

With the Tevatron having made the first precious thousands top quarks,
leading to its discovery and tests of some of its properties,
the LHC is a genuine top quark factory, in particular in Run II, which is now
underway. The data gathered already and especially upcoming data
will allow us to study the top quark and its behavior in LHC collisions
in great detail, if also the theoretical descriptions and simulations
are of commensurate quality.

Here we provide a compact review of some of the key aspects of top quark physics,
largely from a Standard Model point of view.
We highlight key issues from a mostly conceptual standpoint, and list
the present state of affairs in terms of calculations and
corresponding experimental analyses.
We refer to other excellent reviews[5, 6, 7, 8, 9] for
more extensive explanations. In section 2 we discuss mostly
issues regarding properties of the top itself, and characteristics of its decay.
In section 3 we mostly discuss its production, either in
pairs, singly, or in association. We end with a brief conclusion.

2 Top properties and decays

In this first section we give a brief description of how the top quark is embedded in the Standard
Model, and motivates physics beyond it. We also discuss aspects of its
decay and properties such as mass and spin.

2.1 Top in the Standard Model

We recall the various interactions of the top quark field t(x)
in the Standard Model Lagrangian. The interaction with gluons is a vectorlike coupling involving
an SU(3) generator in the fundamental representation

gs¯ti(x)γμ[Ta]ijtj(x)Gaμ(x),

(1)

where i,j label QCD colour charge.
The interaction with photons is also simply vectorlike and proportional
to the top quark electric charge

23e¯t(x)γμt(x)Aμ(x).

(2)

Its charged weak interaction is left-handed and flavour-changing

gw2√2Vtf¯t(x)γμ(1−γ5)f(x)Wμ(x),f=d,s,b,

(3)

while its neutral weak interaction is flavour-conserving and parity violating

gw4cosθW¯t(x)γμ((1−83sin2θW)−γ5)t(x)Zμ(x).

(4)

Finally, the interaction of the top with the Higgs boson is of the Yukawa type

yth(x)¯t(x)t(x),

(5)

with a coupling constant yt=√2mt/v directly proportional
to the top quark mass mt, and v is the Higgs vacuum expectation value.

Beyond these, effective interactions such as for flavour-changing neutral
currents, occur due to loop corrections. They can be calculated and are
generally very small compared to the ones above. All these interactions, either
elementary or effective, could be modified in structure and strength
by virtual effects due to new interactions associated with physics
beyond the Standard Model. This is a particularly interesting line of investigation
for the top quark, if only because it evidently has a large coupling to the electroweak
symmetry breaking sector (the Yukawa coupling yt in Eq. (5) is
almost exactly 1 in the Standard Model). It is then important to test
these structures in detail, and indeed this is the thrust behind the field of top physics.

2.2 Top beyond the Standard Model

Driving most motivations for physics beyond the Standard Model is the
fact that the Higgs mass seems unnaturally small. The top quark features prominently in this
argument as the main culprit for creating this situation.
When considering Standard Model one-loop corrections to the inverse
Higgs boson propagator there are contributions from the W and Z bosons, the Higgs boson itself,
and, most importantly, the top quark. Using an ultraviolet cut-off regulator Λ they
can be added to the bare Higgs mass squared m2H,B to form the renormalized
Higgs mass mH

(6)

Because symmetry is not enhanced by setting
the Higgs mass to zero, renormalization is not necessarily
multiplicative [10], and the divergent corrections
are in fact quadratic in Λ.
Eq. (6) shows that when Λ is of order, say, the GUT
scale, cancellations to many digits are required among these contributions, which
seems a very fine-tuned setup.

Being the main troublemaker, the top may in fact also point to possible
new physics in which this finetuning is avoided. A popular model is
supersymmetry where stop quark loops naturally provide
the cancellations that finetuning does in the Standard Model. But also
in supersymmetry phenomenology the top quark
plays an important role: if it weren’t for the top quark (and stop squark)
corrections to the lightest Higgs boson mass, the Minimal Supersymmetric
Standard Model (MSSM) would predict the latter to be lighter than the Z boson,
and the MSSM would have been ruled out already. The maximum viable mass
for the Higgs mass is thus about 140 GeV, comfortably above the
measured value of 125 GeV.

Top could play an even more central role in the Higgs mechanism, in
that its dominant contribution to the running of a Higgs potential
parameter down from the GUT scale in fact leads to a negative
eigenvalue for the Higgs mass matrix, thereby even explaining electroweak
symmetry breaking [11].

We also note that in the last few years the precise value of the top mass has been
moving further into the spotlight due to its role in regards to the
stability of the electroweak vacuum[12]; the current
value suggests that the vacuum is meta-stable[13, 14, 15, 16].

In short, there is good reason to study the top quark in detail,
what its properties are, how it is produced, and how it decays. We begin
with the latter.

2.3 Top quark decay

The top quark decay characteristics play, directly or indirectly, an important role in
studying the top quark at colliders. The top quark
width is largely due to decays to a W-boson and a
bottom quark. But because the top quark mass is
much larger than the sum of the W and b masses, the width
is sufficiently large to pre-empt top quark hadronization. The rapid
decay of the top quark moreover enables transmision of top quark spin
information to final states, giving us an important tool to test
the role of top quark spin. At the same time, the width-to-mass ratio
Γ/m of the top quark is small enough that, for many purposes, the notion
of top quark as a stable particle makes sense. This is effectively implemented through the
narrow width approximation (NWA), which factorizes the production and
decay processes. But, although the NWA works well for
many, especially inclusive observables, it is still necessary to test its quality
well, given how carefully we aim to study the top quark’s behavior.

The top width itself
is very difficult to determine in a hadron collider,
though a recent experimental inference of the width in the context of single top
t-channel production was performed by D0[17] finding
Γ=2.00+0.47−0.43 GeV, and CDF [18], finding
1.10<Γ<4.05 GeV at the 68% confidence level.
An optimal determination would require a threshold scan for pair production
at a e+e− collider.

The NWA full separation of production and decay is indeed an approximation, and
there are corrections to it. Besides the intrinsic uncertainty of
order Γ/m, there are also non-factorizable corrections
from virtual partons that connect production and decay amplitudes. Another
irreducible class of corrections is from diagrams with the same final
state but having no intermediate top quark.

Let us briefly describe how the NWA works for the decay process of the top quark

t(p)⟶W+(q)+b(r)⟶l+(k1)+ν(k2)+b(r),

(7)

where the top has been produced in the production process

a(P1)+b(P2)⟶t(p)+X(x).

(8)

We shall also see how spin correlations can be included in the NWA.
The squared amplitude for the combined process reads

|A|2

=

g4W|Vtb|2641(p2−m2)2+(mΓ)21(q2−m2W)2+(mWΓW)2

(9)

×

¯¯¯u(r)γμ(1−γ5)(/p+m)MM∗γ0(/p+m)(1+γ5)γρu(r)

×

¯¯¯u(k2)γμ(1−γ5)v(k1)¯¯¯v(k1)(1+γ5)γρu(k2),

where the top and W propagators (and their widths) are shown on the
first line, while the other two lines contain the squared matrix
element for (off-shell) top production, and (off-shell) W decay.
Here M=Γu(K), with Γ a combination of γ-matrices,
and k1,k2 the four-momentum of a fermion entering the hard scattering.

The narrow top width approximation Γ→0 now amounts to
making the replacement

1(p2−m2)2+(mΓ)2⟶πmΓδ(p2−m2),

(10)

yielding an on-shell condition for the top quark momentum p.
Summing over spins one may now write the squared amplitude
in (9) as

∑spin|A|2=πmΓ∑λλ′~Mλρλλ′~M∗λ′δ(p2−m2).

(11)

The matrix ρ is the decay spin-density matrix, encoding spin correlations
between production and decay, with λ,λ′ labelling the top quark
spin states. The above procedure to include
spin correlations in the NWA can be implemented in Monte Carlo programs, even
in those matched to NLO [19, 20, 21]. This works
in many cases very well. Other studies in this regard for t¯t production
can be found in Refs. [[22]] and [[23]].

One should however not take the validity of the NWA for granted for
all observables. Especially for those cases where there is a sizeable
contribution from intermediate top quarks that are not near their mass
shell this is an important issue. In these phase space regions there
can moreover be appreciable contributions from subprocesses producing the same
final state, but having no intermediate top quark.
A recent study [24]
investigated the off-shell effects in t-channel single-top production, in part as
a test of the NWA. Also an effective theory approach
[25] was compared to the exact calculation,
including non-resonant diagrams and off-shell effects in the
[email protected][26] framework using the complex mass scheme
[27, 28, 29].
It was shown that indeed the NWA approximation does
not always work well, in particular for observables sensitive to the W-b invariant mass,
while the effective theory approach does track the exact NLO calculation rather well.

Another NLO study [30] comparing t¯t
production plus decay in the NWA with W+W−b¯b production, the
latter including also singly resonant and non-resonant contributions,
found that these contributions have a signifcant impact on shapes of
distributions, and thereby also the uncertainty of top mass
measurements.

For most of the results discussed below, however, except where stated otherwise,
the NWA is taken, and should be a good approximation.

2.4 The Higgs-top interaction and the W polarization

Top interacts with the Higgs boson through the Yukawa interaction

yth¯tt,

(12)

where yt=√2mt/v. This is a relation that can be kept at the
renormalized level as well, whatever the choice of renormalization
scheme for the top quark mass (about which more below).
As remarked, for the top quark pole mass of about 173 GeV and with v=246 GeV,
yt=1 to a very good approximation.

It is interesting to note that the large Yukawa coupling yt
of the top with the Higgs boson is related to the large fraction
of top quarks decaying into longitudinal W bosons.
In fact, although it is reasonable to expect that in the decay (7)
of a top quark to a W boson, t→W++b, the width be proportional
to the weak coupling g2 and to the top mass, a direct
calculation [31] shows that the expression for the width reads

(13)

with

a=m2t2m2W=y2tg2.

(14)

Note that the width is enhanced by a factor a (about 2.3) with respect to the naive expectation.
Looking at the breakdown of this result to different intermediate W polarizations, we see
that the decay to transversely polarized W bosons is in line with the naive expectation,
while the a enhancement is due to the longitudinal polarization of the W
bosons [31]. In fact, the Goldstone boson equivalence
theorem [32],
which states that the longitudinally polarized W boson acts as a
Goldstone boson (a member of the Standard Model Higgs doublet), predicts
that in the limit mt≫mW the
width of the top decaying into a longitudinal W boson behaves as[33]

Γ(t→W+Lb)∝g2mta.

(15)

We can then write that the fraction of longitudinally polarized W bosons is approximately given by

FL=Γ(t→W+Lb)Γ(t→W+b)≈a1+a.

(16)

Because the ratio a of the squared top and W masses, or equivalently of
the top Yukawa and the gauge couplings, is about 2.3, we expect that about 70%
of the W bosons are longitudinally polarized.
In fact, a precise computation[34] which includes the NNLO QCD corrections as well the
leading electroweak contributions yields FL=0.687(5). This value is well within the experimental error bands,
since an early combination of CDF and D0 Tevatron Run II data[35] yielded FL=0682±0.057,
while CDF[36] obtained FL=0.726±0.094 using the full set of Tevatron Run II data.
At the LHC, CMS has found FL=0.682±0.045 in the 7 TeV run[37], and
FL=0.720±0.054 in the 8 TeV run[38].

2.5 Top mass

The top quark property that is perhaps most central in many aspects of top physics
is its mass. We already mentioned its role in the issue of stability of the
Higgs potential.
From Run I and Run II data and for an integrated luminosity of up to 9.7fb−1,
the Tevatron experiments [39] have measured the mass with a total uncertainty of
0.64 GeV/c2, i.e. to an accuracy of less than 0.4%.
From the run at a centre-of-mass energy of 7 TeV and for an integrated luminosity of up
to 4.9fb−1, the LHC experiments [40]
have measured the mass with a total uncertainty of 0.95 GeV/c2,

CDF/D0:

174.34±0.37(stat)±0.52(sys)GeV/c2,

ATLAS/CMS:

173.29±0.23(stat)±0.92(sys)GeV/c2.

(17)

The Tevatron data from Run II at a centre-of-mass energy of 1.96 TeV and for an integrated luminosity of up to 8.7fb−1
have been combined with the LHC data mentioned above. The resulting worldwide combination is

ATLAS/CDF/CMS/D0:173.34±0.27(stat)±0.71(sys)GeV/c2,

(18)

with a total uncertainty of 0.76 GeV/c2.

CMS [41] has also provided a combination of LHC data from the run at a centre-of-mass energy of 7 TeV
and for an integrated luminosity of up to 5.1fb−1, with the data from the run at a centre-of-mass energy of 8 TeV
and for an integrated luminosity of up to 19.7fb−1, measuring the mass with
a total uncertainty of 0.49 GeV/c2, i.e. to an accuracy of less than 0.3%,

CMS:172.44±0.13(stat)±0.47(sys)GeV/c2.

(19)

Together with an accurately measured W boson mass, a precisely known
top mass severely constrains the mass range of the Higgs boson [42].
Indeed the measured Higgs boson mass seems quite consistent given present accuracies.
Therefore its precise measurement is of considerable importance, and
therefore also its careful definition. This is necessary because for the
top, being coloured and thus subject to confinement, defining the mass
is indeed subtle.

A natural definition of an elementary particle mass is based on the location of the pole of the full
propagator, i.e. the pole mass.
After summing self-energy
corrections the full quark propagator reads

1⧸p−m0−Σ(p,m0),

(20)

where Σ contains 1/ϵ UV divergences from loop integrals.
Renormalization (here at one loop) now amounts to replacing the bare mass m0 by an
expression involving the renormalized mass m

(21)

after which the UV divergences cancel in (20). The choice of zfinite
determines the scheme. Choosing it such that

1⧸p−m0−Σ(p,m0)=c⧸p−m

(22)

is the pole-mass scheme, which amounts to pretending that the particle
can be free and long-lived. However, because
no quark can ever propagate out to infinite times due to confinement,
such a pole only exists in perturbation
theory, and its location is intrinsically ambiguous by O(ΛQCD)[43, 44, 45].

Experimentally, the mass of the top quark is most often reconstructed
by collecting the jets and leptons from its decay. The decay channels used are the dilepton channel - two isolated leptons
with opposite charge and at least two jets[46, 47];
the lepton + jets channel - an isolated lepton and at least four jets[48, 49];
the all-hadronic channel[50, 51].
However, soft particles originating from both within and outside these jets may affect the reconstructed
mass. Moreover, various experimental methods used (e.g. track quality
cuts) and corrections do not have a clean perturbation theory description.
Though it is considered generally a measurement of the pole mass, the full
procedure has led to some discussion about what the precise “scheme”
is of the mass thus measured, and to the possibility
of considering a Monte Carlo mass, which would track closely but not
be
quite the same as the pole mass[52].

Although the experiments in this way reconstruct the pole mass (or something close to it),
theoretically it would be more desirable to have a short-distance mass, free
of O(ΛQCD) ambiguities.
Such is the ¯¯¯¯¯¯¯¯MS mass
¯m(μ), evaluated at some scale μ, whose
relation to the pole mass is known in QCD to three loops analytically[53]
and four loops numerically[54]. For μ
one often takes the implicit value found when intersecting the ¯m(μ)
curve with the ¯m(μ)=μ axis, yielding ¯m(¯m).
The ¯¯¯¯¯¯¯¯MS mass
¯m(μ) may be extracted
indirectly, by comparing, for instance, the measured inclusive cross
section with the theoretical one expressed in the ¯¯¯¯¯¯¯¯MS
mass [55]. Of course, such an indirect measurement will depend upon
the accuracy of the theoretical calculation of the inclusive cross
section, and its sensitivity to the mass.
A recent evaluation by D0 [56] along these
lines yields ¯m(m)=154.5GeV/c2, if the cross section is evaluated to NLO + NNLL
accuracy, [57] or ¯m(m)=160.0GeV/c2, if the cross section is evaluated to NNLO accuracy,
[58, 55] with an uncertainty in both cases of about 5 GeV/c2.

There are other definitions of short-distance masses, inspired by the
top quark pair production near threshold at a future e+e−
collider. One is the 1S mass[59, 60, 61], which is related to the peak position in the
cross section for e+e−→t¯t, and is defined as half the perturbative mass of a fictitious toponium
ground state, where the top quark is assumed to be stable. The relation between the 1S mass and the pole mass
is known to higher orders in QCD. As both the 1S mass and the ¯¯¯¯¯¯¯¯MS mass are short-distance masses,
the relation between them is O(Λ2QCD/m)[60].
At lepton colliders, it might be feasible to determine the 1S top
mass with a precision of about 100 MeV[62] (see this
reference also for an overview of other methods).
Another promising short-distance mass is the potential-subtracted mass [63], which
employs the fact that the IR sensitive part of the pole, discussed in
section 2.3 cancels against the IR sensitivity
of the top-antitop Coulomb potential in threshold production.

Current procedures to measure the top mass are the template method, which uses distributions of top mass values
obtained from the event kinematics, and compares them to distribution templates for reference top mass values, and the
matrix-element method (MEM) [64, 65, 66], which uses the (tree level) matrix elements
to estimate the likelihood of each experimental event for kinematic configurations which come from events of a given top mass.
Improvements of the methods above have been proposed. As regards the former, the template overlap method for infrared safe
jet observables [67] has been put forward, which is based on the fact that the energy flow in jets which come
from the decay of highly boosted top decay products is different from the one in jets which come from the QCD background.
As regards the MEM, the inclusion of QCD radiation effects [68] and the computation of NLO weighted events
[69] have been proposed.

Alternative methods to measure the top mass are also under
consideration. Mostly use proxy variables that are to a varying degree
sensitive to the mass and can be accurately calculated and measured.
One of them uses the leptonic final states of a J/ψ[70]: one may consider the process pp→(t→W++b→W++J/ψ)+(¯t→W−+¯b)
and require that the W− decays hadronically, the W+ decays leptonically and the J/ψ decays into leptons, typically
muons. Then the invariant mass distribution of the J/ψ and an isolated lepton
can be used to evaluate the top mass. Since no jets are involved, the measurement is not plagued by jet energy scale (JES)
uncertainties, which allows for an accurate reconstruction of the mJ/ψl invariant mass, with a projected
O(1GeV) error on the top mass. However, the leptonic decays reduce the rate substantially,
and a large integrated luminosity, of the order of tens of fb−1, is required. The error on the top mass evaluation
can be further improved by including the NLO QCD corrections to production and decay [71].

Some methods use the kinematic distributions of the dilepton channel
to either determine the pole mass while being little sensitive to long-distance effects [72]
or to perform a simultaneous evaluation of the top-quark, W-boson and neutrino masses, basing it
on end-point determinations in the kinematic distributions [73].
This may be convenient in the investigation of
New Physics models, where several masses in a decay chain may be unknown.

Other methods use the invariant mass mt¯t of the t¯t pair [74], or
examine t¯t production in association with a jet [75, 76], and use the invariant mass
mt¯tjet of the t¯t-jet system. These methods complement top mass
measurements from the t¯t total cross section [55, 77, 78].

Finally, a novel method exploits the large top Yukawa coupling to extract the top mass from loop effects in flavour physics
observables [79].

2.6 Spin and angular correlations

Part of the attractiveness of the top quark as a study object is
its power to self-analyze its spin, through its purely left-handed
SM weak decay. This is both a useful aid in signal-background separation,
and itself a property worthy of detailed scrutiny, as certain new physics models
could introduce right-handed couplings. The correlation between top spin and
directional emission probability for its decay products is expressed
through

dlnΓfdcosχf=12(1+αfcosχf),

(23)

where |αf|≤1, with 1 indicating 100% correlation.
Note that in the NWA the correlation between the production process and the spin of the
produced top quark is indicated in eq. (11).
For the dominant decay mode

t→b+W+(→l++ν),

(24)

at lowest order, we have αb=−0.4,αν=−0.3,αW=0.4,αl=1.
QCD corrections to these values are small[80, 81].
The charged lepton direction (or the down-type
quark in a hadronic decay of the intermediate W) is indeed nearly 100% correlated with the
top quark spin. This is notably more than for its parent W boson, a consequence of interference
of two amplitudes with different intermediate W polarizations.

In single-top quark production, which occurs via the charged weak
interaction, the top is produced left-handed, so
a correlation should be a clear feature of the production process
and serve as a discriminant to suppress the background.
In top quark pair production a correlation of an individual quark with a fixed direction
is absent111There is a tiny correlation due Z-boson mediated
production., however there is a clear correlation between the top and anti-top spins. The size of the correlation depends on the choice
of reference axes ^a,^b[82, 83, 84].
At the Tevatron the
beam direction ^a=^b=^p is
good choice, at the LHC the helicity axes
^a=^b=^ktop should give
near-maximal correlation

dσdcosθadcosθb=σ4(1+B1cosθa+B2cosθb−Ccosθacosθb).

(25)

Indeed, the correlation coefficient C depends on the correlation
axis. Thus, at LO in QCD, the values for
{Chel,Cbeam} at the Tevatron (LHC) is
{0.47,0.93} ({0.32,−0.01}). NLO corrections modify these
numbers somewhat [85]. BSM models
that influence the pair production mechanism (e.g. new resonances)
could noticeably influence these correlations.

There is also the interesting possibility of azimuthal
angular distributions as indicators of new physics. Thus, in the
dilepton decay channel, after an invariant mass cut, t¯t
spin correlations may be revealed through the Δϕ
distribution of leptons in the laboratory frame [86]. This
observable is quite robust, as the
correlation remains visible even after summing over spurious neutrino
momentum resolutions, and persists at NLO
[87].

Other angular distributions can function as quite selective probes of
new physics [88, 89].
For instance, if a Z′ would polarize tops at production, the
azimuthal asymmetry

Aϕ=σ(cosϕl>0)−σ(cosϕl>0)σ(cosϕl>0)+σ(cosϕl>0),

(26)

where ϕl is the azimuthal angle of the lepton with respect to
the beam-top plane, would be sensitive to the amount of left-handed and
right-handed coupling, even more so when judicious cuts on the pT of the
top are chosen. When a charged Higgs is present, such an
asymmetry would help distinguish [90, 91]Wt from H−t production.

3 Top production

Having discussed issues concerning top quark decays, we now turn to
aspects of top quark production.
In this section we discuss a number of much studied top quark production
observables. For each we review the theoretical issues, and present experimental status.

3.1 Top pair production cross section

Let us first discuss the cross section measurements from the four experiments that have
collected tops in large quantities. Note that besides cross sections
inferred from specific final states,
combinations are being made that consist of analyses with different final
states, with somewhat different integrated luminosities.

At the Tevatron at 1.96 TeV the measured pair production cross sections, based on
almost all of the collected data, are

CDF:

7.63±0.31(stat)±0.39(sys)±0.15(th)pb,

D0:

7.56±0.20(stat)±0.56(sys)pb,

Tevatroncombined:

7.60±0.20(stat)±0.36(sys)pb.

(27)

The combination shown [92] has a measured uncertainty of
about 5.4%. The best present calculation [93]
yields 7.24+0.23−0.27pb (3.4%).

The measured pair production cross sections by ATLAS and CMS at 7 TeV are

ATLAS:

177±3(stat)±+8−7(sys)±7(lum)pb,

CMS:

166±2(stat)±11(sys)±8(lum)pb,

LHCCombined:

173.3±2.3(stat)±9.8(sys)pb.

(28)

The combined result [94, 95] and its measured uncertainty of
about 5% is to be compared to the best present calculation [93] which
yields 172+6.4−7.5pb (5.7%).

For the 8 TeV data we quote two recent results, for the ATLAS
di-lepton (eμ) for 20.3pb−1, and the CMS di-lepton (eμ) channel for
5.3pb−1, respectively

ATLAS:

242.4±1.7(stat)±5.5(sys)±7.5(lum)pb,

CMS:

239.0±2.6(stat)±11.9(sys)±6.2(lum)pb,

LHCCombined:

241.5±1.4(stat)±5.7(sys)±6.2(lum)pb,

(29)

with an uncertainty of about 3.5% [96, 97]. The
best current calculation [93] yields
245.8+8.8−10.6pb (5.6%). Interestingly, the experimental
uncertainty is now again smaller than the theoretical one, providing a
challenge to theory.

First results at 13 TeV are now appearing, with both CMS
[98] and ATLAS
results, still with large errors, in agreement with theory predictions.

For both colliders and for each collision energy the measurements
are clearly in agreement with each other, and
with the best theoretical calculations, which we
discuss below. The remarkable agreement among different
collision types and energies gives us solid
confidence in the value and structure of the top quark QCD
coupling.

Let us now review the status of, and main ideas behind theoretical
calculations for top quark pair production. The inclusive top
pair production cross section has always played a role that is both useful and
instructive in perturbative QCD, because it only involves QCD
couplings. It moreover features
a truly large produced mass whose effects play a crucial role in
both in the matrix elements and the phase space measure.
The NLO corrections were
computed[99, 100, 101, 102]
in the late 80’s.
For many years these were among the most difficult one-loop
calculations done. In these first calculations phase space was (partially) integrated over
in analytical way; a fully differential calculation
was completed shortly thereafter [103].
The combination of such a fully differential calculation with parton
showers, such as [email protected][104, 105] and
POWHEG[106, 107] is now the state
of art at this order in perturbation theory. These codes
combine the virtues of the exclusiveness of a parton shower event
generator with the accuracy of a NLO calculation.

A recent major development has been the completion of the full NNLO
calculation[108, 109, 110, 93]
for the inclusive pair production cross section.
This is indeed a milestone in top quark physics, even in
perturbative QCD as a whole. The result is a hadronic cross section
computed with a theoretical accuracy at the few percent level, as already mentioned. The
calculations require NNLO corrections to both the q¯q and the gg
channel, as well as the NLO corrections to the
qg channels. For both the q¯q and gg channel, the second
order corrections are composed of three classes of contributions, some
computed at different times by various authors. These are (i) the
two-loop corrections, (ii) the one-loop plus one real emission
correction, and (iii) the double real emission contribution. The
double-real emission calculations were computed earlier
[111, 112, 113]. The one-loop,
one real emission contributions are known, since the NLO calculation
for t¯t+jet is available
[114, 115]. The two-loop virtual
corrections have been performed[116, 117, 118, 119, 120].
The methods used so far are a combination of analytical and numerical
ones. The latter involve solving differential equations in the
kinematic invariants, which requires a highly accurate initial
condition (chosen to be at high energy), and avoiding singularities in
the equations. The double-real emission contribution was achieved
through the use of a method called STRIPPER[111]. The
one-loop, one-real emission diagrams could be computed with
well-established techniques.

The full calculation, altogether a major tour-de-force,
has good perturbative convergence and very
small uncertainties. Given these properties and the excellent
agreement with measurements, as shown in Fig. 1,
a comparison of theory and data for
the inclusive cross section can be used more prosaically to infer useful knowledge about
the gluon density. A first study in this direction was done
[121], demonstrating the feasibility and desirability of this.
The top cross section has now been included in the NNPDF3.0 global fit [122].

Figure 1: Data and theory for the inclusive top quark pair production cross
section at Tevatro and LHC as function of the
collider c.m. energy, compared to recent measurements of ATLAS
and CMS, compiled by the Top Physics LHC Working Group.

Electroweak corrections to top pair production have also been computed
[123, 124, 125], which can be
large in certain phase space regions, depending on transverse
momentum. They can also impact the charge asymmetry [126].
Calculations including off-shell
effects are beginning to appear as well [25, 127].

On top of the exactly calculated orders one can add arbitrarily high orders in
approximately using threshold resummation.
The latter also underlies some theoretical estimates of the top
quark charge asymmetry, discussed in section
3.2, as well as various distributions,
so let us review this method briefly here.

When the top quark pair is produced near threshold in hadronic collisions, logarithms
whose argument represents the distance to threshold in the perturbative
series become numerically large.
The definition of the threshold depends on the observable. Thus,
for the inclusive cross section the threshold is given by the condition
T1:s−4m2=0. For the transverse momentum distribution we have
T2:s−4(m2+p2T)=0, and for the doubly differential distribution in
pT and rapidity we can choose

T3:s−4(m2+p2T)coshy=0orT3:s+t+u−2m2=0.

(30)

The perturbative
series for any of these (differential) cross sections can be in
general expressed as

diσ(Ti)=∑n2n∑kαnscin,klnk(Ti),

(31)

plus non-logarithmic terms.
Here Ti represents any of the threshold conditions, suitably
normalized, for the observables
enumerated by i. Note that it is allowed to use e.g. T2 for the
inclusive cross section, by first analyzing dσ/dpT and then integrating
over pT, and similarly for T3. For any complete fixed order calculation this will give the same
answer, but if one only selects the logarithmic terms because the exact answer
is unknown, numerical differences will occur. Such kinematic
differences can then be viewed as theoretical uncertainties [128].

The threshold logarithms result from integration over phase space
regions where the emitted gluons are soft and/or collinear to their on-shell emitter.
Resummation concerns itself with carrying out the sum in
Eq. (31), and the result takes the generic form

dσ=exp(Lg0(αsL)+g1(αsL)+αsg2(αsL)+…)×C(αs).

(32)

Including up to the function gi in the exponent amounts to NiLL
resummation, with the coefficient C(αs) then evaluated
to order i−1. Key benefits of threshold resummation are (i) gaining all-order control of the
large terms which plague
fixed-order perturbation theory, to restore predictive
power, and (ii) reduction of scale uncertainty. Regarding the first
point, the reason these resummable terms are large for the top quark
pair inclusive cross section is that, while
the hadronic cross section is Sudakov suppressed near threshold,
the PDF’s are over-suppressed, which the
partonic cross section must then partially compensate for.
Regarding the second point, when examining the
sources of scale dependence, they occur both in the PDF and in
the partonic cross section now both in the exponent, which
improves the cancellation[129].

The state-of-the-art accuracy for threshold resummation for
inclusive pair production cross section at present is NNLL
[130, 131, 132, 133]. A consistent combination of
NNLL accuracy in both threshold and Coulomb corrections has now also
been achieved [77]. The latter are
only relevant for threshold T1 and behave as (αs/β)n, with
β2=1−4m2/s. From such all-order results, approximate NNLO results were
constructed before the completion of the exact calculation.
This is of particular interest for thresholds T1 and T3.
The latter, being dependent on t and u, then allows estimating
threshold resummation corrections to the forward-backward
asymmetry, a point we return to in section
3.2.
Other approximate NNLO calculations use threshold T3 and results
based on these [133] are typically larger than for T1, closer to
the exact result; estimates are also made for approximate NNNLO[134].
As mentioned above, calculations using T3 can
assign ambiguities due to using either pair-invariant mass (PIM) or
one-particle inclusive (1PI) kinematics in the precise definition of
the threshold to a theoretical error [128, 78].

The various theoretical calculations are available in a number of
codes, such as HATHOR[135]
(contains full NNLO corrections, and possibility of using a running
top quark mass), TOP++[136]
(contains full NNLO corrections, and NNLL threshold resummation),
TOPIXS [137] (contains NLO, approximations
for NNLO, and NNLL resummation, including Coulomb corrections).

In the above, the top quarks are treated as on-shell stable
particles, using the narrow-width approximation.
It is interesting to include in the full description also
the top quark decays, including the effects of off-shellness and
spin-correlations. Thus, one considers then as final state of interest
WWbb. For zero b-quark mass two groups have computed the NLO corrections
to this production process [138, 127],
establishing an interesting tool to study such effects.

3.2 Charge asymmetry

A different test of the QCD production mechanism of top quarks, one that has received
much attention in recent years, is the charge asymmetry: the normalized difference in
production rate between top and anti-top at some fixed angle or rapidity

At(y)=Nt(y)−N¯t(y)Nt(y)+N¯t(y).

(33)

While electroweak production via a Z-boson could produce a (very small) asymmetry at LO, QCD itself
produces it at O(α3s) through a term proportional
to the SU(3) dabc
symbol [100, 102, 139, 114].
A more precise look [139] shows that the asymmetry is due
to an interference between C-odd and C-even terms. In top quark
pair production in the q¯q channel this amounts to the Born
diagram and the one-loop box diagram, respectively.
When computing such an interference contribution, the asymmetry reveals
itself in terms of the Mandelstam variables t and u as terms that are odd under
t↔u interchange, e.g. t2−u2.
In t¯t plus 1 jet production an asymmetry can already occur at tree
level (essentially, this amounts to a different cut of the same
amplitude). Measurements [140, 141, 142, 143]
by the Tevatron experiments show
substantial deviations from the Standard Model prediction for pair
production, especially a deviation of more than 3 standard deviations
by CDF at large invariant t¯t masses [141].
For this reason there has been considerable interest in this observable.

We discuss here the Standard Model calculations for this observable.
A discussion of the many studies of specific New Physics effects on
the charge or forward-backward asymmetry is beyond the scope of this review.

The effect of this interference can be understood more intuitively
by the statement that the incoming quarks, via the
interference, tend to repel the produced top quarks towards larger
rapidity, and/or attract the produced anti-top quarks toward slightly
smaller rapidities. The net effect, therefore, at the Tevatron, where
the top- anti-top pairs are produced in q¯q annihilation, is a
shift of the top quark rapidity distribution towards larger rapidity,
and of the anti-top distribution towards smaller values. This clearly
creates a y-dependent asymmetry of the type (33). Because of
these shifts, this also corresponds to a forward-backward asymmetry AFB.

This intuition may also be obtained in threshold resummation
from the so-called soft anomalous dimension in the q¯q channel, which governs
subleading threshold logarithms; leading logarithms are symmetric under
t↔u interchange, and therefore cancel in the
asymmetry. The subleading contribution in the q¯q channel reads [144]

Δσ=exp{αsL[326−276]lnut}σBorn,

(34)

where L is the threshold logarithm. This expression, through
ln(u/t), is indeed anti-symmetric under t↔u
interchange.

Since the leading contribution to this effect for NLO pair production involves
a loop diagram, the asymmetry itself is then of leading order
accuracy. The impact of even higher orders is then very
interesting. They have first been estimated from approximate,
resummation based calculations to NLL
[145, 128] and NNLL
[146, 147, 148].
For this only resummations based on
threshold T3, see Eq. (30), can be used, as the other two thresholds
are not sensitive to the top quark rapidity. The higher order
corrections so computed are small,
and reasonably insensitive to scale variations.
Hence, based on these approximate calculations, the discrepancy
would persist, although in recent
analyses by D0 [149, 150] it is found to be not so
large.

For the t¯t case the electroweak corrections have been calculated
[151, 152, 126]. They are
unexpectedly
large, thus also diminishing the overall discrepancy.
It is worth noting that, from a slightly different perspective, effects of colour reconnection in
parton shower algorithms can already cause an asymmetry
at what is formally leading order [153].

Very recently the exact calculations for the charge asymmetry
to NNLO were completed [154]. Upon taking into account
the second order QCD corrections in addition to the first order EW
corrections a shift of no less than 27% with respect to the NLO QCD asymmetry was
found, yielding a value of AFB=0.095±0.007. This is now in
good agreement with the most recent
D0 measurement of 0.106±0.03[155],
and only somewhat below the CDF [156] value of 0.164±0.047,
which seems to settle this issue to a large extent.

Besides defining the asymmetry in terms of the top quark itself
(33), one may define it also in terms of the leptons produced
in top and/or anti-top decay , either in the lepton-plus-jets or the di-lepton
channel. The AllFB asymmetry will be in general a little washed out, but leptons
are relatively easy to measure. There is however still a need
for unfolding due to limited acceptance.
A recent compilation of theory predictions including leptonic
asymmetries is available[151].

At the Tevatron, CDF and D0 have performed a set of measurements for
various types of asymmetries. At the constructed top quark level
the measured asymmetries exceed the theory prediction by a few
standard deviations.
We already mentioned the top quark level asymmetries by D0 and CDF.
Recent AllFB measurements in the lepton-plus-jets channels corrected to
the parton level are 16.4±4.7% (CDF) and
12.6±6.5% (D0), vs. 8.8±0.6% according to the SM.
An overview can be found in Ref. [[157]].

As noted above, the charge asymmetry is present at leading order in
t¯t+jet production. However, here NLO corrections
[114, 115] tend to wash out the asymmetry for
this reaction. An explanation for this effect was given in
Ref. [[115]], based on the following structure of the NLO
forward-backward asymmetry for this reaction

AFB(t¯tj)=α3sCln(m/pT,j)+α4sDhard.

(35)

The second term, appearing at NLO, cancels the first as they
have opposite signs. The inverse logarithm is due to the fact that the
denominator in the asymmetry has a higher power of leading soft logarithms.
Also for t¯tjj the NLO term seems to reduce the LO contribution
to the asymmetry [158].

At the LHC, the net effect of the QCD induced asymmetry is an overall broadening of the top quark
rapidity distributions and a slight narrowing of the anti-top rapidity
distribution. Here there is therefore no forward-backward asymmetry,
but a charge asymmetry that is most pronounced at larger rapidities. One proposal [159]
is e.g. to assess the asymmetry using only events with (anti)tops
above a certain minimum rapidity, of about 1.5.
New observables with promising sensitivity have been proposed[160, 161].

At 7 TeV, a combination of CMS and ATLAS measurements[162, 163]
of the charge asymmetry yields 0.005±0.007(stat)±0.006(syst),
in agreement with the NLO QCD and electroweak theory[126],
although also compatible with a lack of asymmetry.

3.3 Invariant mass and other distributions

Besides inclusive observables such as the cross section and charge
asymmetry, differential distribution afford a more detailed look
into production dynamics. For instance, a moderate enhancement
in tails of distributions due to New Physics would possibly not be visible
in the inclusive observables.
An important distribution for both the Tevatron and the LHC is
in the invariant mass Mt¯t. The shape of the distribution in
the SM has a relatively small uncertainty. It has been computed in
approximate NNLO in resummed NNLL accuracy [57].

It is sensitive to the top mass, and may thus assist in determining
it. Shape deviations from the QCD predictions in this distribution
(peaks, peak-dip structures) are telltales of new physics, such as
resonances with various spin, parity and colour quantum numbers. A
study employing the flexibility of MadGraph in a bottom-up approach
was performed in Ref. [[74]], in which only the most
generic aspects of new models are used.
Given that the exact charge asymmetry calculation [154] was
based on a fully differential NNLO calculation for pair production, various
differential distributions will soon be available at that accuracy.

Approximate calculations based on resummation methods, discussed earlier, have
already been done, e.g. for the invariant mass distribution
[164], and for single particle inclusive
distributions at the NNLO and beyond level
[165, 166, 131].

Measurements of differential distributions in variables
associated with the top quark pair have been performed, as
well as of single particle inclusive distributions
[167, 168, 169, 170, 171].

3.4 Single top production

Tops can be produced singly through the weak interaction, in
processes that are customarily categorized
by names referring to kinematics in the Born approximation,
see Fig. 2.

Figure 2: From left to right the s-channel (1), t-channel (2) processes,
and the Wt associated (3) production
channel.

Important aspects of single-top production are
that Vtb can be directly measured without assuming three fermion
generations, and that the chiral
structure of the associated vertex can be tested. The latter is the case
because a single top produced in this way
is highly polarized, which offers a chance to study the chirality of the coupling
via spin correlations, as discussed in eq. (11),
section 2.3.
Another feature is that the dominant t-channel at the LHC, when
confronting measurements with a 5-flavour NLO calculation,
will help determine the b-quark density. (In a 4-flavour scheme, one
would demand an extra forward (b) jet).
Finally, it is interesting that the different single top production processes
are each sensitive to different varieties of new physics.
Thus, the s-channel will be sensitive to e.g. W′ resonances, the t-channel to FCNC’s.
Note that the channel separation according to Fig. 2 holds to NLO,
but not to all orders; at higher orders interference can take place between
channels. Let us however maintain this separation, and discuss the channels
separately.

3.4.1 s and t channel

Experimentally, both of these single top
production processes turned out to be rather more difficult to
separate from backgrounds than expected, as the latter are large,
and similar in shape to the signals.
Based on samples of up to 9.7 fb−1 per experiment,
the Tevatron combination[172] of a number of CDF and D0 measurements yields an
inclusive single top production cross section of

σ=3.30+0.52−0.40pb,

(36)

and a measurement of |Vtb|=1.02+0.06−0.05.
Furthermore, CDF and D0 have reported the Tevatron combination[173] of inclusive single top production
in the s channel only, with a cross section of

σs=1.29+0.26−0.24pb.

(37)

At the LHC at a centre-of-mass energy of 7 TeV,
the inclusive SM production rates of the s-channel, t-channel and Wt channel
are approximately 4.6, 65 and 16 pb respectively; at 8 TeV they are 5.6, 88 and 22 pb, respectively.
The t-channel yields clearly the dominant contribution. Besides interesting
in its own right, the t-channel process is a background to many new physics
processes involving both neutral and charged Higgs production.
Based on samples of 4.6 fb−1 by ATLAS and 1.14 fb−1 by CMS
of the run at 7 TeV,
the t-channel cross section is [174, 175]

ATLAS:

σt=68±2(stat)±8(sys)pb,

CMS:

σt=67.2±3.7(stat)±4.8(sys)pb.

(38)

Based on samples of 20.3 fb−1 by ATLAS and 19.7 fb−1 by CMS
of the run at 8 TeV, the t-channel cross section is [176, 177]

ATLAS:

σt=82.6±1.2(stat)±12.0(sys)pb,

CMS:

σt=83.6±2.3(stat)±7.4(sys)pb.

(39)

A combination, based on partial data samples of 5.8 fb−1 by ATLAS and 5.0 fb−1 by CMS,
yields [178]

ATLAS/CMS:σt=85±4(stat)±11(sys)±3(lumi)pb,

(40)

with a total uncertainty of 12.1 pb, and in good agreement with the SM prediction.
For all the measurements above, the values of Vtb which are extracted are compatible with 1.

Based on the sample of 20.3 fb−1 of the run at 8 TeV, ATLAS has found a first evidence of
s-channel production[179] at 3.2σ level

ATLAS:σs=4.8±1.1(stat)+2.2−2.0(sys)pb.

(41)

On the theory side, the single top cross section has been computed at NLO accuracy in the QCD and electroweak
corrections [180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 25, 24], including
resummations [193, 194, 195, 196] and
matching NLO computations to parton showers [197, 198, 199];
and at NNLO accuracy in the QCD corrections [200].
The NLO (and NNLO) corrections are at a few percent level, and within errors
the measured cross sections agree with them. Approximate NNLO pT
distributions have recently appeared [201, 202].

3.4.2 Wt associated production

A subtle and interesting issue arises in the Wt mode of single top production at NLO.
In the radiative corrections some diagrams contain an
intermediate anti-top decaying into a W and anti-down type quark, that can become resonant.
From another viewpoint, these diagrams can be interpreted as LO t¯t on-shell
production, with subsequent ¯t decay, see Fig. 3.

One is therefore faced with the issue to what extent the Wt and
t¯t can be properly defined and separated as individual processes.
To this end several definitions of the Wt channel have been given in the literature,
each with the aim of recovering a well-behaved expansion in αs. This problem
of interference is of course not uncommon in computations
at order of at least O(g2wα2s). The
cross section at this order has been previously presented in
Refs. [[203, 204, 205]], where only
tree-level graphs were considered, and in
Refs. [[206, 187, 207]], where one-loop
contributions were included as well. The rather vexing point here is
that the t¯t process with which the Wt interferes is an order of
magnitude larger, rendering the NLO correction much too large.

In Ref. [[208]] this interference issue was addressed
extensively in the context of event generation, in particular the
[email protected] framework (POWHEG has implemented
the same method [209]). Two different procedures for subtracting the doubly-resonant contributions
and thereby recovering a perturbatively well-behaved Wt cross section
were defined. In “Diagram Removal (DR)” the graphs in
Fig. 3 were eliminated from the calculation, while in “Diagram Subtraction (DS)”
the doubly resonant contribution was removed via a judiciously constructed subtraction term.
The DS procedure leads to the following expression for the cross section

dσ(2)+∑αβ∫dx1dx2x1x2SLαβ(^Sαβ+Iαβ+Dαβ−~Dαβ)dϕ3,

(42)

where αβ labels the initial state channel in which
the doubly-resonant contribution occurs: ggorq¯q.
^S is the square of the non-resonant diagrams,
I their interference with D, the square of
graphs of Fig. 3. The subtraction term ~D requires
careful construction [208].
It was shown that, with suitable cuts, the interference terms are small.
From Eq. (42) one sees that the
difference of DR and DS in essence consists of the interference term.
A particularly suitable cut is imposing a maximum on
the pT of the second hardest b-flavoured hadron,
a generalization of a proposal made in Ref. [[187]].
Thus defined, the Wt and t¯t cross sections
can be separatedly considered to NLO.

The experimental status of this production mode at present
is as follows. In the 7 TeV run, ATLAS [210] and CMS
[211] have measured the Wt-channel cross
section, with the results

ATLAS[2.05fb−1]:

σWt=16.8±2.9(stat)±4.9(sys)pb,

CMS[4.9fb−1]:

σWt=16+5−4pb.

(43)

In the 8 TeV run, a combination of Wt-channel measurements has been performed[212, 213],
based on a data set of 12.2 fb−1 by CMS and 20.3 fb−1 by ATLAS

One way to avoid the above difficulties in separating Wt from
¯tt is to consider the common final state WWbb (in the
4-flavour scheme) and not ask
if there were one or two intermediate top quarks involved in producing
this final state – zero intermediate top quarks is also a possibility here.
In Refs. [[216, 217]] a unified approach
in the 4-flavour scheme was taken in which both Wt and
¯tt produce as final state WWbb, and the NLO corrections were
computed.

3.5 Associated top production at higher order

One can also consider processes where a top pair
or a single top are produced in association with other particles.
Given its relevance for the measurement of the Higgs-top Yukawa coupling,
clearly the most important associated production is the production of a top pair in
association with a Higgs boson, t¯th. This process is known to NLO accuracy
in QCD, at parton level [218, 219] and interfaced to
parton showers [220, 221]. Also the electroweak
corrections have been computed [222, 223].

The rapid evolution of computations of scattering processes with many
final-state particles to NLO accuracy in QCD – the so-called NLO revolution –
has left its mark on processes involving top production as
well, yielding calculations that would have been hard to imagine some years ago.
Accordingly, many important backgrounds to top pair production in association with a Higgs boson,
with subsequent decay of the Higgs boson into a bottom-quark pair or into a pair of photons,
have been computed to NLO accuracy. In particular,
production of a top pair in association with a jet is known to NLO accuracy at parton level [114, 115],
including the top decays [224], as well as non-resonant diagrams, interferences and off-shell
effects[225], and interfaced with parton showers [226, 227, 228];
top pair production in association with two jets is known to NLO accuracy at parton level [229, 158],
and interfaced with parton showers [230]; production of a top pair in association with a b¯b pair
is known at parton level [231, 232, 233] and interfaced with parton
showers [234, 235, 236];
production of a top pair in association with a photon is known to NLO accuracy at parton level [237]
and interfaced with parton showers [26, 238];
production of a top pair in association with two photons is known to NLO accuracy at parton level and interfaced with parton
showers [26, 239].

Furthermore, the production of a top pair in association with a Z boson is known to NLO accuracy
at parton level [240, 241]
and interfaced with parton
showers [242, 243], which is relevant to
measure the t¯tZ coupling [244, 245];
the production of a top pair in association with a W boson is known to NLO accuracy [246, 247, 248]
and interfaced with parton showers [243], which can be used as a tool to examine the top-quark charge asymmetry.
Also the electroweak corrections to the production of a top pair in association with a W/Z boson have been computed [223].
The production of a top pair in association with two vector bosons, be it either W,Z bosons or photons,
is known to NLO accuracy at parton level, and interfaced with parton showers [26, 249];
as well as the production of a top pair in association with a vector boson and a jet
is known to NLO accuracy at parton level, and interfaced with parton showers [26].
Finally, the production of two top pairs is known to NLO accuracy at parton level [250, 249],
which can be used as a benchmark process to test New Physics signals.

In addition, single top production in association with a W boson is known to
NLO accuracy at parton level [208, 217],
and interfaced to parton showers [208],
which is relevant for the Wt mode of single top production, see Sect. 3.4.2;
single top production in association with a Z boson is known to
NLO accuracy at parton level [251],
which is a background to flavour changing neutral current decays of the top in t¯t production.
Various single top production processes in association with a b quark and a Z boson or a photon
or a jet are available to NLO accuracy in Ref. [[26]].

4 Conclusions

Top quark physics is at present at a pivotal point,
in the early days of Run II of the LHC. Rather accurate
studies of top quark observables from Tevatron and LHC Run I
data have been done, but the bulk of (higher energy) data
is still to be collected. Also in top physics the Standard
Model has withstood tests so far, but many highly detailed and varied
tests by the LHC experiments will follow.

Top’s attractiveness as a study object has by
no means diminished. On the contrary, new observables
are being enlisted for this enterprise. The characteristics
of production and decay, in association with other
particles, can be very revealing. The examination of
many (multi-)differential distributions,
a full accounting of spin and off-shellness, and especially
its interaction with the Higgs boson are all still to come.

As we have reviewed here, the theoretical tools for top physics studies
are of high quality, and still keep improving with remarkable pace. We are
therefore confident that the top quark will remain in the focus
of attention for a good many more years.

Acknowledgments

We would like to thank F. Maltoni and M. Vreeswijk for valuable
discussions and comments.
EL has been supported by the Netherlands Foundation for Fundamental
Research of Matter (FOM) programme 156, entitled “Higgs as Probe and Portal”,
and the National Organization for Scientific Research (NWO).
This work was also supported by the Research Executive Agency (REA)
of the European Union under Grant Agreement numbers
PITN-GA2012-316704 (HiggsTools), and
PITN-GA-2010-264564 (LHCPhenoNet).